Put the flour into a saucepan. Gradually add the milk. Cook over medium to high heat, stirring constantly until thickened. Pour mixture through strainer to be sure there are no lumps. Cool.
Whip the butter, shortening and sugar together. Then whip in cooled flour/milk mixture. Add vanilla and beat on high until fluffy. Recipe produces a white icing. (7-10 minutes)
Recipe and image taken with permission fromVi Whittington and Autumn Carpenter's Book, Creative Cupcakes.